Linear and nonlinear AC response of Abrikosov vortices in layered superconductors adiabatic approximation

Abstract

Linear and nonlinear AC responses for a magnetically coupled stack of two-dimensional vortices (2DV's) forming an Abrikosov vortex line perpendicular to the layers of a layered superconducting film are calculated. By solving the Fokker-Planck equations for the distribution functions of 2DV positions in the adiabatic approximation and including randomly distributed pinning centers, a nonlinear differential equation for the continuous shift function S( z, t) is derived. Josephson coupling only changes coefficients in this equation. The equation for S( z, t) is solved perturbatively for the linear AC response and for the third-order mixing current at frequency 2ω 1-ω 2. This pseudoharmonic mixing probes the nonlinearity of the intervortex force and its interplay with pinning. Explicit analytical results are given for the surface impedance Z s and the mixing current δ j( 3). The cases of thin and thick films with respect to the AC penetration length are considered in detail.